A system is tested for faults once per hour. If there is no fault, none will be detected. If there is a fault, the probability is 0.8 that it will be detected. The tests are independent of one another.
a. If there is a fault, what is the probability that it will be detected in 3 hours or less?
b. Given that a fault has gone undetected for 2 hours, what is the probability that it will be detected in the next hour?
c. What is the mean number of tests that must be conducted in order to detect a fault?